Article excerpt

1. Introduction

Problem solving and decision making are universally considered to be the skills that play the most important role for each manager. The range of problems that present-day manager has to face is extremely wide, including typical tasks that can be solved by standard techniques, as well as unique issues requiring individual approaches. The generally accepted typology of decisions proposed by Simon (1965) includes programmed and non-programmed. Programmed decisions are routine. They rely on some form of predetermined procedures which are invoked when a particular problem occurs. Non-programmed decisions are those for which such procedural guides don't exist. In practice, however, managers often have to face problems that include both typical and unique elements.

One of the most important features of managerial decisions is multidimensionality. In order to make a decision a manager has to consider multiple criteria, including quantitative and qualitative ones. It is also pointed out that decision-making is usually associated with some degree of risk. The process of globalization and fast technological development result in the increasing level of uncertainty that managers have to face. Thus, the need for developing and practical implementation of new decision aiding techniques dedicated for managerial decision making problems appear.

One of the most difficult problem that we have to solve implementing multicriteria techniques is identification of the decision maker preferences. Usually he/she is not able to express precisely and unequivocally his/her expectations with respect to the solution of the problem. In such case interactive techniques can be used. While it is difficult for the decision maker to provide the whole preference information required for constructing the complete ranking of decision alternatives, he/she usually is able to compare selected solutions.

Most of interactive techniques are devoted to decision-making problems under certainty. Unfortunately, as was mentioned above, risk cannot be ignored, when a real-world decision problem is considered. This was the motivation for the author to propose new interactive techniques devoted for decision-making problems under risk. The aim of this paper is to present such techniques and to discuss potential applications in operations management.

The paper is structured as follows. Section 2 provides problem formulation and concise survey of techniques used for solving it. Section 3 presents a brief survey of interactive techniques used for solving decision making problems under certainty. Next section is dedicated to stochastic dominance rules that can be used to compare uncertain projects. In section 5 interactive procedures for discrete multicriteria decision making problems under risk are proposed. Applications of these techniques in managerial decision making problems are discussed in section 6. The last section groups conclusions.

2. A discrete decision-making problem under risk

This paper considers a decision-making problem in which the set of alternatives consists of a finite number of elements that are explicitly described. We assume that up to moderate number of alternatives (not more than one hundred) are considered. Alternatives are evaluated with respect to a finite number of multiple criteria (not less than three and not more than ten). As a decision-making problem under risk is analyzed here, so we assume that the evaluations of alternatives with respect to criteria are described by probability distributions.

The decision situation considered in this paper may be conceived as a problem (A, X, E) where A is a finite set of alternatives [a.sub.i], i = 1, 2, ..., m; X is a finite set of criteria [X.sup.k], k = 1, 2, ..., n; and E is a set of evaluations of alternatives with respect to criteria: